8.7.29 problem 54

Internal problem ID [835]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 54
Date solved : Monday, January 27, 2025 at 03:09:29 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(4*x^2*diff(y(x),x$2)+8*x*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_2 \,x^{2}+c_1}{x^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

DSolve[4*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^2+c_1}{x^{3/2}} \]